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- Publisher Website: 10.1007/BF01262989
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Article: Circulant integral operators as preconditioners for Wiener-Hopf equations
Title | Circulant integral operators as preconditioners for Wiener-Hopf equations |
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Authors | |
Keywords | AMS(MOS) Subject Classifications: 45E10, 45L10, 65R20, 65J10 |
Issue Date | 1995 |
Citation | Integral Equations and Operator Theory, 1995, v. 21, n. 1, p. 12-23 How to Cite? |
Abstract | In this paper, we study the solutions of finite-section Wiener-Hopf equations by the preconditioned conjugate gradient method. Our main aim is to give an easy and general scheme of constructing good circulant integral operators as preconditioners for such equations. The circulant integral operators are constructed from sequences of conjugate symmetric functions {Cτ}τ. Let k(t) denote the kernel function of the Wiener-Hopf equation and {Mathematical expression} be its Fourier transform. We prove that for sufficiently large τ if {Cτ}τ is uniformly bounded on the real line R and the convolution product of the Fourier transform of Cτ with {Mathematical expression} uniformly on R, then the circulant preconditioned Wiener-Hopf operator will have a clustered spectrum. It follows that the conjugate gradient method, when applied to solving the preconditioned operator equation, converges superlinearly. Several circulant integral operators possessing the clustering and fast convergence properties are constructed explicitly. Numerical examples are also given to demonstrate the performance of different circulant integral operators as preconditioners for Wiener-Hopf operators. © 1995 Birkhäuser Verlag. |
Persistent Identifier | http://hdl.handle.net/10722/276734 |
ISSN | 2023 Impact Factor: 0.8 2023 SCImago Journal Rankings: 0.654 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Chan, Raymond H. | - |
dc.contributor.author | Jin, Xiao Qing | - |
dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:34:29Z | - |
dc.date.available | 2019-09-18T08:34:29Z | - |
dc.date.issued | 1995 | - |
dc.identifier.citation | Integral Equations and Operator Theory, 1995, v. 21, n. 1, p. 12-23 | - |
dc.identifier.issn | 0378-620X | - |
dc.identifier.uri | http://hdl.handle.net/10722/276734 | - |
dc.description.abstract | In this paper, we study the solutions of finite-section Wiener-Hopf equations by the preconditioned conjugate gradient method. Our main aim is to give an easy and general scheme of constructing good circulant integral operators as preconditioners for such equations. The circulant integral operators are constructed from sequences of conjugate symmetric functions {Cτ}τ. Let k(t) denote the kernel function of the Wiener-Hopf equation and {Mathematical expression} be its Fourier transform. We prove that for sufficiently large τ if {Cτ}τ is uniformly bounded on the real line R and the convolution product of the Fourier transform of Cτ with {Mathematical expression} uniformly on R, then the circulant preconditioned Wiener-Hopf operator will have a clustered spectrum. It follows that the conjugate gradient method, when applied to solving the preconditioned operator equation, converges superlinearly. Several circulant integral operators possessing the clustering and fast convergence properties are constructed explicitly. Numerical examples are also given to demonstrate the performance of different circulant integral operators as preconditioners for Wiener-Hopf operators. © 1995 Birkhäuser Verlag. | - |
dc.language | eng | - |
dc.relation.ispartof | Integral Equations and Operator Theory | - |
dc.subject | AMS(MOS) Subject Classifications: 45E10, 45L10, 65R20, 65J10 | - |
dc.title | Circulant integral operators as preconditioners for Wiener-Hopf equations | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/BF01262989 | - |
dc.identifier.scopus | eid_2-s2.0-0039838010 | - |
dc.identifier.volume | 21 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 12 | - |
dc.identifier.epage | 23 | - |
dc.identifier.eissn | 1420-8989 | - |
dc.identifier.isi | WOS:A1995QF23800002 | - |
dc.identifier.issnl | 0378-620X | - |